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14091991
@14091991
July 2022
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[tex] \int\limits^ \frac{pi}{2} _0 { cos^{2} x} \, dx [/tex]
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svetic71
У cos сначала нужно понизить степень по формуле сos²x=(1+cos2x)/2=1/2+1/2cos2x
∫(1/2+1/2cos2x)=1/2x+1/4sin2x=1/2·π/2+1/4sin(2·π/2)-1/2·0-1/4sin2·0 =
π/4+1/4sin π -0=π/4+1/4·0=π/4
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Answers & Comments
∫(1/2+1/2cos2x)=1/2x+1/4sin2x=1/2·π/2+1/4sin(2·π/2)-1/2·0-1/4sin2·0 =
π/4+1/4sin π -0=π/4+1/4·0=π/4